Vacuum Persistence Amplitude and Gravitational Potential in $f(R)$ Gravity

TL;DR

This paper uses source theory to derive the gravitational potential between two static masses in a specific modified gravity model, $f(R)=R+aR^2$, extending methods from Einstein gravity.

Contribution

It applies the vacuum-to-vacuum transition amplitude approach to $f(R)$ gravity, providing a new way to compute gravitational potentials in modified theories.

Findings

Derived the gravitational potential for two static masses in $f(R)=R+aR^2$ gravity.

Extended source theory methods from Einstein gravity to $f(R)$ models.

Demonstrated the applicability of vacuum transition amplitudes in modified gravity contexts.

Abstract

The source theory provides a straightforward way to obtain the Newton's potential upon establishing the vacuum-to-vacuum transition amplitude in quantized Einstein theory of gravity. Here, we use the same method to derive the gravitational potential of two static point masses in $f(R)=R+aR^2$ gravity.